R program for MLE parameter estimation

Per the model and dataset definitions described below, I need an complete R program which:

1. generates a dataset (or utilize some existing dataset) comprising of one explanatory (x) value & one response (y) value for each case in the dataset.

2. declares an appropriate log-likelihood function(s) for the model

3. optimizes the log-likelihood function based on the dataset... resulting in the calculation of a Maximum Likelihood parameter estimate for "b".

Model / Dataset Description:


1. A Dataset comprising of one explanatory variable (x) and one response variable (y) for each case in the dataset.

2. Model must be of the following functional form:

x^b = y

Solve for "b" using Maximum Likelihood parameter estimation

Skills: Data Mining, Machine Learning, Scientific Research, Statistics

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